<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-04-24</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001487999</issuerCik>
        <issuerName>SeaCube Container Leasing Ltd.</issuerName>
        <issuerTradingSymbol>BOX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001380393</rptOwnerCik>
            <rptOwnerName>Fortress Investment Group LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001387345</rptOwnerCik>
            <rptOwnerName>FIG Corp.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001245521</rptOwnerCik>
            <rptOwnerName>FIG LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001387344</rptOwnerCik>
            <rptOwnerName>Fortress Operating Entity I LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001411588</rptOwnerCik>
            <rptOwnerName>Seacastle Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001493163</rptOwnerCik>
            <rptOwnerName>Seacastle Operating Co Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001360379</rptOwnerCik>
            <rptOwnerName>Fortress Investment Fund IV (Fund A) L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001360424</rptOwnerCik>
            <rptOwnerName>Fortress Investment Fund IV (Fund D) L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001371234</rptOwnerCik>
            <rptOwnerName>FORTRESS FUND III GP LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001371238</rptOwnerCik>
            <rptOwnerName>Fortress Investment Fund III LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1345 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-04-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>8525000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Seacastle Operating Company Ltd.</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Seacastle Operating Company Ltd. is wholly owned by Seacastle Inc. Seacastle Inc. is wholly owned by Fortress Investment Fund III LP, Fortress Investment Fund III (Fund B) LP, Fortress Investment Fund III (Fund C) LP, Fortress Investment Fund III (Fund D) L.P., Fortress Investment Fund III (Fund E) L.P., Fortress Investment Fund III (Coinvestment Fund A) LP, Fortress Investment Fund III (Coinvestment Fund B) LP, Fortress Investment Fund III (Coinvestment Fund C) LP and Fortress Investment Fund III (Coinvestment Fund D) L.P. (collectively, the &quot;Fund III Funds&quot;), Fortress Investment Fund IV (Fund A) L.P., Fortress Investment Fund IV (Fund B) L.P., Fortress Investment Fund IV (Fund C) L.P., Fortress Investment Fund IV (Fund D) L.P., Fortress Investment Fund IV (Fund E) L.P., Fortress Investment Fund IV (Fund F) L.P., Fortress Investment Fund IV (Fund G) L.P., Fortress Investment Fund IV (Coinvestment Fund A) L.P., (Continued in Footnote 2)</footnote>
        <footnote id="F2">(Continued from Footnote 1) Fortress Investment Fund IV (Coinvestment Fund B) L.P., Fortress Investment Fund IV (Coinvestment Fund C) L.P., Fortress Investment Fund IV (Coinvestment Fund D) L.P., Fortress Investment Fund IV (Coinvestment Fund F) L.P. and Fortress Investment Fund IV (Coinvestment Fund G) L.P. (collectively, the &quot;Fund IV Funds&quot;), and certain members of Seacastle Inc.'s management. Fortress Fund III GP LLC is the general partner of each of the Fund III Funds. The sole managing member of Fortress Fund III GP LLC is Fortress Investment Fund GP (Holdings) LLC. The sole managing member of Fortress Investment Fund GP (Holdings) LLC is Fortress Operating Entity I LP (&quot;FOE I&quot;). FIG Corp. is the general partner of FOE I, and FIG Corp. is wholly owned by Fortress Investment Group LLC. (Continued in Footnote 3)</footnote>
        <footnote id="F3">(Continued from Footnote 2) Fortress Fund IV GP L.P. is the general partner of each of the Fund IV Funds. Fortress Fund IV GP Holdings Ltd. is the general partner of Fortress Fund IV GP L.P. Fortress Fund IV GP Holdings Ltd. is wholly owned by FOE I. FIG Corp. is the general partner of FOE I. FIG Corp. is wholly owned by Fortress Investment Group LLC. FIG LLC is the investment manager of each of the Fund III Funds and each of the Fund IV Funds.</footnote>
    </footnotes>

    <remarks>Form 1 of 2:

The Form is the first of two being filed by Fortress Investment Group LLC.  Two Forms are being filed as there are more than ten joint filers. Filers on the second of the two Forms are: Fortress Investment Fund GP (Holdings) LLC, Fortress Fund IV GP L.P. and Fortress Fund IV GP Holdings Ltd.  The Reporting Persons no longer beneficially own 10% of the Issuer's Shares and are no longer subject to Section 16.</remarks>

    <ownerSignature>
        <signatureName>/s/ David N. Brooks, Secretary of Fortress Investment Group LLC</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ David N. Brooks, Secretary of FIG Corp.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ David N. Brooks, Secretary of FIG LLC</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: FIG Corp., its General Partner, By: /s/ David N. Brooks, Secretary of FIG Corp.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Chris Annese, as Authorized Signatory of Seacastle Inc.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Chris Annese, as Authorized Signatory of Seacastle Operating Company Ltd.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: Fortress Fund IV GP L.P., its General Partner, By: Fortress Fund IV GP Holdings Ltd., its General Partner, By: /s/ David N. Brooks, Secretary of Fortress Fund IV GP Holdings Ltd.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: Fortress Fund IV GP L.P., its General Partner, By: Fortress Fund IV GP Holdings Ltd., its General Partner, By: /s/ David N. Brooks, Secretary of Fortress Fund IV GP Holdings Ltd.</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ David N. Brooks, Secretary of Fortress Fund III GP LLC</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: Fortress Fund III GP LLC, its General Partner, By: /s/ David N. Brooks, Secretary of Fortress Fund III GP LLC</signatureName>
        <signatureDate>2013-04-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
